Questions tagged [math]

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6
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4answers
2k views

Interview Question - Card betting

I had to answer questions for a job interview today and I got these questions. I had no idea how to answer them. There is a deck of 12 cards numbered 1 to 12. One card is pulled from the deck at ...
5
votes
1answer
832 views

Pre-requisite math books, to the pre-requisite math needed to become a front desk quant

This question is about the pre-requisites to the pre-requisite math needed to become a front desk quant. I have done research online and I found that there are a lot of recommended books as a pre-...
3
votes
1answer
159 views

Finding optimal trading of option on a foward

Assume you have a option on a forward $F$ with a payoff: $\max(F_T - K, 0)$. Assume also, that you have a bullish view on the forward in such a way that $E_{0}[F_T] > F_0 = E_{0}^{*}[F_T]$ (where ...
3
votes
1answer
175 views

Mark Joshi, The concepts and practice of mathematical finance chapter 6 exercise 20,21

Find the Black-Scholes price of an option paying $$(S_T^{\alpha} - K)_{+}$$ at time $T$. Solution - The forward price is given by $$F_T(t) = e^{r(T-t)}S_t$$ So, $$F_T(0) = e^{rT}S_0$$ and $...
2
votes
0answers
94 views

How do i calculate Monthly French Fama RMW and CMA?

I have tried to transform the values from daily $R^d_t$ to weekly $R_t^w$ by calculating the cumulative return: $$RMW_t^w = \left[\left(\frac{RMW_1}{100} + 1\right)\left(\frac{RMW_2}{100}+1\right)...\...
1
vote
2answers
203 views

How much shall we bet on head/tail with $1m bankroll?

I was asked this question in a trading interview: how much would you bet in a game where you win 300 on tail and loses your 100 on heads? how much will you bet if you can play game once or multiple ...
1
vote
1answer
49 views

Calculating coupon yield and continous compounding

I need to calculate the yield of a 2 year Coupon Bond. Price = 98, Coupon = 3.5, N = 100. Now when I try to solve this, I arrive at the equation: $$ 98 = 3,5*e^{-y}+103,5*e^{-2*y} $$ But I can't ...
1
vote
1answer
3k views

Given two risky stocks calculate the rate of return, standard deviation, beta, and risk-free rate

Consider a world where there are only two risky stocks, $A$ and $B$, whose details are listed in the table below: Furthermore, the correlation between the returns of stocks $A$ and $B$ is $\rho_{A ...
1
vote
1answer
72 views

Implied Expected Stock Return from European Option Prices

We can calculate the expected stock return (under the measure $Q$) from at-the-money ($K=S_t$) option prices as: $$E\left(\frac{S_T-S_t}{S_t}\right)=\frac{e^{rT}}{S_t}(C_t-P_t)$$ The result is ...
1
vote
1answer
123 views

Dice question - expected winnings of rolling dice $2$ times

Typical trading interviews consider gambling problems such as rolling a dice and winning its face value. The expected winnings are $\\\$3.5$, $\\\$4.25$, $\\\$\frac{14}{3}$ for one throw, two throws, ...
1
vote
1answer
62 views

Determine the error term of SKEW-calculation

I am trying to recreate the CBOE's SKEW Index in Python. I need to calculate the errors terms that are adjustment terms for the differences between the atm strike ...
1
vote
1answer
58 views

partial derivatives of multivariable function

Looking to verify whether the following formulation is correct. Suppose we have the following function, relationships: $$y=f(x)$$ $$x=g(a,b)$$ $$y=f[g(a,b)]$$ Is the below correct (including ...
1
vote
1answer
49 views

Why the variance of a process is $\left( \frac{dS_T^2}{dt}\right)^2$?

Consider an Ito process $dS_t = f(t,S_t) dt + g(t,S_t)dW_t $ What is the reason that we can compute the variance as: $\sqrt{VaR(S_t)} = \frac{(dS_t)^2}{dt}$
1
vote
1answer
48 views

How is hypothesis testing work in population sampiling? [closed]

I am learning the basics of quant trading from quantconnect's tutorial Confidence Interval and Hypothesis Testing. I understood the first part of the article but I dont understand "Hypothesis Testing"...
1
vote
1answer
72 views

Finding the extrinsic value of an option with conditions

Background: Consider a spread option with the payoff $\max (P_{T} - HR\times G_T, 0)$, where $P$, $G$ are underlying prices and $HR$ is a constant. Let's also assume, that the correlation ...
1
vote
0answers
164 views

How to compute prediction interval if using simple moving average t o predict?

If I want to use simple moving average to make a prediction. For example given h=1 and m=13. $\hat{x}_{t+1}=\frac{\sum_{j=1}^{13}x_{t-j+1}}{13}$. What is the prediction interval going to be? How to ...
1
vote
0answers
37 views

Residual Income Valuation with Term Structure

I'm implementing a residual income model (RIM) to value stocks as described by Ohlson. https://pdfs.semanticscholar.org/c0a5/4ef41311951fe406d15cd7d7ce19502cdc7c.pdf The key to this model is ...
1
vote
0answers
45 views

Evaluating contract $D$ where the stock follows the Black Scholes assumption

Ch.7 Mark Joshi Problem 14 A contract, $D$, pays $30\%$ of the increase (if any) of a stock's value in a year. If $S_t$ follows Black-Scholes assumptions, give a formula in terms of the Black-...
1
vote
0answers
89 views

Moving average variance [closed]

I have generated a random series of returns drawn from a normal distribution and generated a random price series by compounding these returns (X) so $P_i = P_1(1+X)^i$. I want to show the analytic ...
1
vote
0answers
223 views

What jobs in Finance are most math intensive? [closed]

I'm a math major and I've always been really interested in Finance; however, I'm starting to enjoy math more and more and would like to know which jobs in Finance use the most/more advanced math. Also,...
0
votes
1answer
242 views

Joshi, Exercise 2.7 Concepts of Mathematical Finance

Let $D(K)$ pay $(S - K)^2$ if $S > K$, zero otherwise. Show that if $D(K)$ is differentiable function of $K$ then the third derivative w.r.t $K$ is non-negative. From what the hint in the book, we ...
0
votes
1answer
90 views

Properties of Brownian motion and filtration, Exercise 6.22, Joshi Concepts and applications to mathematical finance

Let $W_t$ be a Brownian motion, and let $F_t$ be its filtration then for $t > s$ we are asked to compute $$\mathbb{E}\left[W_t^2|F_s\right]$$ We have $$W_t = W_s + (W_t - W_s)$$ and $$W_t^{2} ...
0
votes
1answer
371 views

Using CAPM to derive the following

Background Information: Say there are $s = 1,\ldots,S$ possible future outcomes (states) with known probabilities $\pi_s > 0$, $\sum_{s=1}^{S}\pi_s = 1$. Define the expected payoff as $\mathbb{E}_\...
0
votes
1answer
62 views

Bachelier call option derivative w.r.t strike

I tried to take the partial derivative of the Bachelier call function w.r.t. strike price K (eqn 2.2 here), but my result is not lining up with what is shown on page 43 here.
0
votes
1answer
40 views

Price of every asset in discrete market model strictly increasing

If the price of every asset in a discrete model is strictly increasing, with probability one, then does the market admit arbitrage? Thoughts: I believe this is true but I am not sure how to give an ...
0
votes
1answer
350 views

Generate Monte Carlo simulation of multivariate lognormal or weibull distributions in R

I intend to perform a Monte Carlo simulation of asset returns in R. I am currently using the rmvnorm function in the mvtnorm R ...
-1
votes
2answers
136 views

Given three stocks what is the fraction of each stock's risk is diversified away

Consider an equally weighted portfolio of three stocks, each of which is independently distributed of the others but have the same risk. I.e., $cov(r_i, r_j) = 0$; $\forall i \neq j$, and $\...
-2
votes
1answer
307 views

How to solve $dX_t = X_t(\sigma_t dW_t + \mu_t dt)$?

Solve the SDE $$dX_t = X_t(\sigma_t dW_t + \mu_t dt)$$ where $\sigma_t$,$\mu_t$ are deterministic. Attempted solution We have $$dX_t = X_t(\sigma_t dW_t + \mu_t dt)$$ Let $f(x) = \log X$, applying ...